{"created":"2023-07-27T06:52:08.037230+00:00","id":45885,"links":{},"metadata":{"_buckets":{"deposit":"ab88cd7c-8b2d-4c24-987c-dcfd1d8e0564"},"_deposit":{"created_by":18,"id":"45885","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"45885"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00045885","sets":["2812:2813:2817"]},"author_link":["2873","79714"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2017-06-02","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"5p.","bibliographicVolumeNumber":"2013-04-01 - 2017-03-31","bibliographic_titles":[{"bibliographic_title":"平成28(2016)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2016 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Ito, Hidekazu"}],"nameIdentifiers":[{"nameIdentifier":"79714","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"90159905","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=90159905"}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"可積分系および通常よりも過剰な個数の第一積分をもつ超可積分系の大域的な解構造に関わる諸問題を，平衡点など不変集合に付随する共鳴現象との関わりで研究した。とくに，偶数次元の解析的ベクトル場が楕円型平衡点の近傍で，平衡点の共鳴度に応じた個数の第一積分と可換なベクトル場をもつならば，解析的なポアンカレ－デュラック標準化が可能であることを示した。これは先行研究の仮定を部分的に一般化した上で別証明を与えたものになっている。 また，共鳴度に応じた個数の第一積分をもつ超可積分な解析的シンプレクティック写像では，線形部分に半単純性を課すことなく，解析的バーコフ標準化ができることを示した。","subitem_description_type":"Abstract"},{"subitem_description":"We studied various problems concerning the global structure of solutions for integrable systems and superintegrable systems possessing larger number of integrals. The resonance among eigenvalues of linearized dynamics associated with invariant sets such as equilibria played an important role in this study. In particular, we studied an even dimensional analytic vector field near an elliptic equilibrium point and showed that there exists an analytic transformation which takes the vector field into Poincare-Dulac normal form, provided that there exist a sufficient number (associated with the resonance degree) of integrals and commuting vector fields. This gives an alternative proof of a known result under weaker assumptions in a special case. Also, we succeeded in showing that a superintegrable symplectic map can be taken analytically into Birkhoff normal form without assuming semi-simplicity of its linear part.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:25400108, 研究期間(年度):2013-04-01 - 2017-03-31","subitem_description_type":"Other"},{"subitem_description":"出典：「退化可積分系の摂動問題と共鳴現象の数理」研究成果報告書　課題番号25400108\n（KAKEN：科学研究費助成事業データベース（国立情報学研究所））\n（https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400108/25400108seika/)を加工して作成","subitem_description_type":"Other"}]},"item_9_description_5":{"attribute_name":"提供者所属","attribute_value_mlt":[{"subitem_description":"金沢大学理工研究域数物科学系","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00052219","subitem_identifier_reg_type":"JaLC"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/search/?qm=90159905"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=90159905","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25400108/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25400108/","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400108/25400108seika/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-25400108/25400108seika/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"伊藤, 秀一"}],"nameIdentifiers":[{"nameIdentifier":"2873","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"90159905","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=90159905"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-09-28"}],"displaytype":"detail","filename":"SC-PR-ITO-H-kaken 2017-5p.pdf","filesize":[{"value":"172.3 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-ITO-H-kaken 2017-5p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/45885/files/SC-PR-ITO-H-kaken 2017-5p.pdf"},"version_id":"4e322f25-6d51-4d5f-962c-515d542cd027"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"退化可積分系の摂動問題と共鳴現象の数理","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"退化可積分系の摂動問題と共鳴現象の数理"},{"subitem_title":"Perturbation problems for degenerate integrable systems and mathematics for resonance phenomena","subitem_title_language":"en"}]},"item_type_id":"9","owner":"18","path":["2817"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-10-01"},"publish_date":"2018-10-01","publish_status":"0","recid":"45885","relation_version_is_last":true,"title":["退化可積分系の摂動問題と共鳴現象の数理"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2024-07-01T05:39:23.271945+00:00"}